This time around the case involved a representation of the commandments that was to be placed on the grounds of the Indiana Statehouse.
The justices let stand a lower-court injunction that blocked the placement of the monument.
The case was only the latest in a stream of similar disputes that have been individually and consistently rejected by the high court over the last few years.
Last year the Supreme Court refused to review of a case out of Indiana involving a Ten Commandments monument banned from the lawn of a municipal building.
Rehnquist argued unsuccessfully that the depiction of the commandments in a public place simply recognizes that they "have made a substantial contribution to our secular legal codes."
Four of the nine justices must vote to take a case before it can be argued before the Supreme Court.
In the case rejected Monday, Indiana Gov. Frank O'Bannon in March 2000 approved a monument donated by the Indiana Limestone Institute for display on the Statehouse lawn.
The monument featured the Ten Commandments, the Bill of Rights and the preamble to the 1851 Indiana Constitution.
The monument was intended to replace a previous Ten Commandments monument placed on the lawn in 1958 by the Fraternal Order of Eagles -- following a promotional campaign for Cecille B. deMille's 1956 movie, "The Ten Commandments."
That earlier monument had been vandalized. Indiana told the Supreme Court that Stephen Schroeder was convicted of spray-painting, breaking and toppling that first representation.
However, a group of challengers, including Schroeder and the Indiana Civil Liberties Union, filed suit in federal court in May 2000. The challengers argued that the proposed placement of the monument violated the separation of church and state guaranteed by the First Amendment.
A federal judge issued an injunction against its placement, saying O'Bannon's explanation of the secular purpose of the monument was "a disingenuous sham," in the words of the Indiana brief to the Supreme Court.
When a federal appeals court agreed 2-1, Indiana asked the Supreme Court for review, saying the First Amendment should permit "the government to display the Ten Commandments to memorialize the role the commandments have played in the development of the rule of law and of the American legal system."
The justices rejected the case Monday in a one-line order.
The consistency of the Supreme Court in rejecting a stream of such cases carries with it a certain irony.
The Ten Commandments are depicted in the justices' courtroom. On a large frieze high above the spectators, Moses is one of a series of lawgivers, and is holding the tablets.
Even more prominently, two tablets with numbers one to 10 in Roman numerals is on the frieze high above the bench, where it can be seen by most spectators.
Supreme Court guides explain the tablets as "the Bill of Rights."
(No. 01-966, Gov. O'Bannon vs. ICLU et al)
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